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Fermat’s principle (Exercise 64) also explains why light rays traveling between air and water undergo bending (refraction). Imagine that we have two uniform media (such as air and water) and a light ray traveling from a source
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- What will be the answer to the questionarrow_forwardThe two-dimensional wave equation describing the vibrations of an infinite string is 2²n_ 20²m Ət² əx² where n = n(x, t), -∞ 0 is a constant. (i) Show that the general solution can be written as n(x, t) = F(x - ct) + G(x + ct) with F and G arbitrary functions. Explain the physical interpretation of F and G in the overall shape of the string. (ii) If the string's initial position is given by n(x, t = 0) = 1 1+4x² velocity by (x, t = 0) = 0 determine F, G and hence n(x, t). Ət (iii) Now consider a semi-infinite string 0 0. If at t = = 0 the string is at rest and has displacement n(x, t 0) = x(5x)e-², find F, G and hence n(x, t), stating clearly the solution for x ct.arrow_forwardA particle is acted upon by constant forces 4i+j-3k and 3i+j-k and is displaced from the point (1,2,3)to the point (5,4,1). Find the total work spent by the forces ?arrow_forward
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